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Inhomogeneous magnetic fields produce artifacts in MR images including signal dropout and spatial distortion. A novel perturbative method for calculating the magnetic field to first order (error is second order) within and around nonconducting objects is presented. The perturbation parameter is the susceptibility difference between the object and its surroundings (for example, approximately 10 ppm in the case of brain tissue and air). This method is advantageous as it is sufficiently accurate for most purposes, can be implemented as a simple convolution with a voxel-based object model, and is linear. Furthermore, the method is simple to use and can quickly calculate the field for any orientation of an object using a set of precalculated basis images.
Jenkinson et al. (Mon,) studied this question.